Airfoil shape for a turbine rotor blade

ABSTRACT

A turbine rotor blade is provided including an airfoil having an airfoil shape. The airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.

FIELD

The present invention relates to an airfoil for a turbine rotor blade of a stage of a turbine and particularly relates to a shape defining a profile for an airfoil of a turbine rotor blade.

BACKGROUND

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., stator vanes or nozzles and rotor blades.) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages are set forth below in the following description, or may be obvious from the description, or may be learned through practice.

An aspect of the present invention may be embodied by a turbine rotor blade including an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.

An aspect of the present invention may be embodied in a turbine rotor blade including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

An aspect of the present invention may be embodied in a turbine comprising a turbine wheel having a plurality of turbine rotor blades, each of the turbine rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape.

Those of ordinary skill in the art will better appreciate the features and aspects of such embodiments, and others, upon review of the specification.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of various embodiments, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, including reference to the accompanying figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including alternating rows of turbine rotor blades and stationary vanes or nozzles according to at least one embodiment of the present disclosure; and

FIG. 2 is a perspective view of a turbine rotor blade according to at least one embodiment of the present disclosure.

DETAILED DESCRIPTION

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of turbine nozzles or vanes disposed axially adjacent to a corresponding row of turbine rotor blades. Four stages are illustrated in FIG. 1. The exact number of stages of the turbine 10 is a choice of engineering design, and may be more or less than the four stages illustrated in FIG. 1. The four stages are merely exemplary of one turbine design, and are not intended to limit the presently claimed turbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14. The turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 200 may be coupled to a casing 16 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 300 may be coupled to the casing 16 of the turbine 12. In particular embodiments, the turbine 12 includes a fourth stage which includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. The fourth stage turbine nozzles 400 may be coupled to the casing 16 of the turbine 12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a hot gas path 18 of the turbine 12. The various stages of the turbine 10 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine rotor blade 50 as may be incorporated in any stage of the turbine 12. For example, in one embodiment the turbine rotor blade 50 as presented in Table I below is representative of a turbine rotor blade 250 of the plurality of turbine rotor blades 250 of the second stage. As shown in FIG. 2, the turbine rotor blade 50 includes an airfoil 52 having a pressure-side wall 54 and an opposing suction-side wall 56. The pressure-side wall 54 and the suction-side wall 56 meet or intersect at a leading edge 58 and a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure and suction-side walls 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.

The airfoil 52 includes a root or first end 64 which intersects with and extends radially outwardly from a base or platform 66 of the turbine rotor blade 50. The airfoil 52 terminates radially at a second end or radial tip 68 of the airfoil 52. The pressure and suction-side walls 54, 56 can be said to extend in span or in a span-wise direction 70 between the root 64 and/or the platform 66 and the radial tip 68 of the airfoil 52. In other words, each turbine rotor blade 50 includes an airfoil 52 having opposing pressure and suction-side walls 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise 70 between the root 64 and the radial tip 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 72 formed between the platform 66 and the airfoil 52 proximate to the root 64. The fillet 72 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 72. In particular embodiments, the platform 66, airfoil 52 and the fillet 72 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered. In particular configurations, the turbine rotor blade 50 includes a mounting portion 74 which is formed to connect and/or to secure the turbine rotor blade 50 to the rotor shaft 14.

The airfoil 52 of the turbine rotor blade 50 has a profile at any cross-section taken between the platform 66 or the root 64 and the radial tip 68. The X, Y, and Z values are given in Table I as percentage values of the airfoil length or height/span. As one example only, the height or radial span of the airfoil 52 of turbine rotor blade 50 may be from about 10 inches to about 40 inches. However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

A gas turbine hot gas path requires airfoils that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine rotor blade airfoil, there is a unique set or loci of points in space that meet the stage requirements and that can be manufactured. This unique loci of points meets the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system and are not obvious to those skilled in the art.

The loci which defines the airfoil profile of turbine rotor blade 50 comprises a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the airfoil profile of the turbine rotor blade 50 at various locations along its length and height or radial span. Table I lists data for a non-coated airfoil, and the envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location. A point data origin 76 is defined at or proximate to the root 64 at the leading edge 58. In one embodiment as presented in Table I below, the point data origin 76 is defined at or proximate to (above or below) a transition or intersection line 78 defined between the fillet 72 and the airfoil 52. The point data origin 76 corresponds to the non-dimensional Z value of Table I (presented below) at Z equals 0.

The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the airfoil height in Table I although other units of dimensions may be used when the values are appropriately converted. The X, Y, and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the airfoil 52 height or radial span 70. To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table I is multiplied by the Z length of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies generally parallel to a centerline of the rotor shaft 14, i.e., the rotary axis and a positive X coordinate value is axial toward an aft, i.e., exhaust end of the turbine 10. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the radial tip 68. All the values in Table I are given at room temperature and do not include the fillet 72.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the airfoil 52 of the turbine rotor blade 50, at each Z distance along the length of the airfoil 52 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil 52. As the turbine rotor blade 50 heats up during operation of the gas turbine 12, surface stress and temperature will cause a change in the X, Y and Z's. Accordingly, the values for the profile given in Table I represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil 52. Each cross-section is joined smoothly with the other cross-sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular turbine rotor blade 50 airfoil design and turbine 12, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in Table I below at the same temperature. The data provided in Table I is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below a 3000-3600 RPM range. The design of the airfoil 52 for turbine rotor blade 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I Suction-side Pressure-side X (%) Y (%) Z (%) N X (%) Y (%) Z (%) 0.0000 0.0000 0.0000 1 0.0000 0.0000 0.0000 −0.3895 0.7151 0.0000 2 0.4741 −0.3831 0.0000 −0.5020 1.5243 0.0000 3 1.0407 −0.6129 0.0000 −0.4142 2.3392 0.0000 4 1.6441 −0.7127 0.0000 −0.2003 3.1309 0.0000 5 2.2562 −0.7119 0.0000 0.0974 3.8947 0.0000 6 2.8643 −0.6393 0.0000 0.4597 4.6305 0.0000 7 3.4637 −0.5132 0.0000 0.8699 5.3408 0.0000 8 4.0519 −0.3448 0.0000 1.3192 6.0271 0.0000 9 4.6305 −0.1437 0.0000 1.8005 6.6903 0.0000 10 5.2027 0.0758 0.0000 2.3113 7.3328 0.0000 11 5.7733 0.2977 0.0000 2.8460 7.9545 0.0000 12 6.3464 0.5156 0.0000 3.4022 8.5571 0.0000 13 6.9226 0.7247 0.0000 3.9777 9.1421 0.0000 14 7.5012 0.9250 0.0000 4.5682 9.7111 0.0000 15 8.0830 1.1173 0.0000 5.1748 10.2642 0.0000 16 8.6672 1.3017 0.0000 5.7965 10.7989 0.0000 17 9.2538 1.4781 0.0000 6.4342 11.3152 0.0000 18 9.8428 1.6449 0.0000 7.0870 11.8117 0.0000 19 10.4350 1.8037 0.0000 7.7550 12.2873 0.0000 20 11.0287 1.9529 0.0000 8.4389 12.7406 0.0000 21 11.6249 2.0934 0.0000 9.1381 13.1700 0.0000 22 12.2235 2.2235 0.0000 9.8508 13.5754 0.0000 23 12.8244 2.3440 0.0000 10.5778 13.9545 0.0000 24 13.4270 2.4541 0.0000 11.3192 14.3073 0.0000 25 14.0311 2.5547 0.0000 12.0726 14.6305 0.0000 26 14.6377 2.6433 0.0000 12.8380 14.9250 0.0000 27 15.2450 2.7215 0.0000 13.6153 15.1891 0.0000 28 15.8540 2.7885 0.0000 14.4014 15.4206 0.0000 29 16.4645 2.8428 0.0000 15.1979 15.6185 0.0000 30 17.0750 2.8859 0.0000 16.0016 15.7837 0.0000 31 17.6872 2.9170 0.0000 16.8109 15.9138 0.0000 32 18.2993 2.9354 0.0000 17.6257 16.0088 0.0000 33 18.9122 2.9409 0.0000 18.4437 16.0678 0.0000 34 19.5243 2.9338 0.0000 19.2642 16.0910 0.0000 35 20.1365 2.9138 0.0000 20.0838 16.0782 0.0000 36 20.7486 2.8803 0.0000 20.9026 16.0287 0.0000 37 21.3591 2.8340 0.0000 21.7191 15.9441 0.0000 38 21.9689 2.7733 0.0000 22.5299 15.8236 0.0000 39 22.5770 2.6983 0.0000 23.3352 15.6680 0.0000 40 23.1828 2.6105 0.0000 24.1333 15.4781 0.0000 41 23.7869 2.5084 0.0000 24.9226 15.2546 0.0000 42 24.3887 2.3919 0.0000 25.7023 14.9992 0.0000 43 24.9872 2.2618 0.0000 26.4701 14.7111 0.0000 44 25.5826 2.1173 0.0000 27.2259 14.3919 0.0000 45 26.1740 1.9593 0.0000 27.9681 14.0431 0.0000 46 26.7622 1.7869 0.0000 28.6967 13.6656 0.0000 47 27.3464 1.6018 0.0000 29.4102 13.2610 0.0000 48 27.9258 1.4022 0.0000 30.1077 12.8300 0.0000 49 28.4996 1.1891 0.0000 30.7901 12.3743 0.0000 50 29.0694 0.9633 0.0000 31.4557 11.8955 0.0000 51 29.6337 0.7247 0.0000 32.1038 11.3927 0.0000 52 30.1915 0.4733 0.0000 32.7342 10.8683 0.0000 53 30.7446 0.2083 0.0000 33.3472 10.3224 0.0000 54 31.2913 −0.0678 0.0000 33.9417 9.7574 0.0000 55 31.8316 −0.3567 0.0000 34.5188 9.1740 0.0000 56 32.3655 −0.6576 0.0000 35.0774 8.5738 0.0000 57 32.8923 −0.9697 0.0000 35.6193 7.9577 0.0000 58 33.4126 −1.2929 0.0000 36.1445 7.3272 0.0000 59 33.9258 −1.6265 0.0000 36.6528 6.6840 0.0000 60 34.4326 −1.9713 0.0000 37.1468 6.0295 0.0000 61 34.9322 −2.3264 0.0000 37.6273 5.3639 0.0000 62 35.4246 −2.6911 0.0000 38.0950 4.6903 0.0000 63 35.9090 −3.0646 0.0000 38.5515 4.0088 0.0000 64 36.3871 −3.4485 0.0000 38.9960 3.3192 0.0000 65 36.8579 −3.8412 0.0000 39.4302 2.6233 0.0000 66 37.3208 −4.2418 0.0000 39.8547 1.9210 0.0000 67 37.7765 −4.6512 0.0000 40.2690 1.2131 0.0000 68 38.2251 −5.0686 0.0000 40.6744 0.5004 0.0000 69 38.6656 −5.4940 0.0000 41.0710 −0.2179 0.0000 70 39.0998 −5.9266 0.0000 41.4597 −0.9401 0.0000 71 39.5259 −6.3663 0.0000 41.8420 −1.6664 0.0000 72 39.9449 −6.8125 0.0000 42.2163 −2.3958 0.0000 73 40.3575 −7.2658 0.0000 42.5842 −3.1285 0.0000 74 40.7622 −7.7255 0.0000 42.9465 −3.8651 0.0000 75 41.1604 −8.1915 0.0000 43.3017 −4.6042 0.0000 76 41.5515 −8.6632 0.0000 43.6512 −5.3464 0.0000 77 41.9362 −9.1397 0.0000 43.9952 −6.0910 0.0000 78 42.3136 −9.6225 0.0000 44.3336 −6.8388 0.0000 79 42.6840 −10.1101 0.0000 44.6680 −7.5874 0.0000 80 43.0487 −10.6026 0.0000 44.9968 −8.3392 0.0000 81 43.4062 −11.0998 0.0000 45.3208 −9.0926 0.0000 82 43.7574 −11.6018 0.0000 45.6409 −9.8484 0.0000 83 44.1022 −12.1085 0.0000 45.9569 −10.6049 0.0000 84 44.4413 −12.6185 0.0000 46.2682 −11.3639 0.0000 85 44.7741 −13.1333 0.0000 46.4046 −11.6999 0.0000 86 44.9186 −13.3615 0.0000 46.4916 −11.9162 0.0000 87 45.0120 −13.5092 0.0000 46.5786 −12.1325 0.0000 88 45.1038 −13.6568 0.0000 46.6656 −12.3488 0.0000 89 45.1955 −13.8045 0.0000 46.7518 −12.5658 0.0000 90 45.2873 −13.9529 0.0000 46.8380 −12.7821 0.0000 91 45.3775 −14.1014 0.0000 46.9242 −12.9992 0.0000 92 45.4685 −14.2498 0.0000 47.0096 −13.2155 0.0000 93 45.5666 −14.3935 0.0000 47.0950 −13.4326 0.0000 94 45.6903 −14.5156 0.0000 47.1612 −13.6560 0.0000 95 45.8348 −14.6129 0.0000 47.1716 −13.8883 0.0000 96 45.9944 −14.6816 0.0000 47.1229 −14.1157 0.0000 97 46.1636 −14.7191 0.0000 47.0176 −14.3232 0.0000 98 46.3376 −14.7223 0.0000 46.8627 −14.4964 0.0000 99 46.5084 −14.6903 0.0000 46.6704 −14.6265 0.0000 100 46.6704 −14.6265 0.0000 −0.0152 0.9234 10.0000 1 −0.0152 0.9234 10.0000 −0.3935 1.6449 10.0000 2 0.4613 0.5275 10.0000 −0.4852 2.4581 10.0000 3 1.0359 0.2953 10.0000 −0.3783 3.2721 10.0000 4 1.6488 0.1971 10.0000 −0.1468 4.0599 10.0000 5 2.2698 0.1971 10.0000 0.1708 4.8172 10.0000 6 2.8867 0.2721 10.0000 0.5507 5.5451 10.0000 7 3.4948 0.4014 10.0000 0.9785 6.2466 10.0000 8 4.0918 0.5762 10.0000 1.4453 6.9226 10.0000 9 4.6784 0.7813 10.0000 1.9449 7.5746 10.0000 10 5.2618 0.9976 10.0000 2.4733 8.2043 10.0000 11 5.8460 1.2091 10.0000 3.0255 8.8125 10.0000 12 6.4334 1.4126 10.0000 3.5986 9.4014 10.0000 13 7.0231 1.6089 10.0000 4.1891 9.9729 10.0000 14 7.6161 1.7965 10.0000 4.7949 10.5267 10.0000 15 8.2115 1.9761 10.0000 5.4174 11.0630 10.0000 16 8.8093 2.1468 10.0000 6.0567 11.5802 10.0000 17 9.4094 2.3081 10.0000 6.7111 12.0766 10.0000 18 10.0128 2.4605 10.0000 7.3815 12.5507 10.0000 19 10.6177 2.6026 10.0000 8.0678 13.0024 10.0000 20 11.2251 2.7350 10.0000 8.7702 13.4294 10.0000 21 11.8348 2.8563 10.0000 9.4876 13.8300 10.0000 22 12.4469 2.9681 10.0000 10.2195 14.2027 10.0000 23 13.0599 3.0678 10.0000 10.9657 14.5459 10.0000 24 13.6760 3.1564 10.0000 11.7263 14.8579 10.0000 25 14.2929 3.2338 10.0000 12.4988 15.1381 10.0000 26 14.9106 3.2985 10.0000 13.2825 15.3847 10.0000 27 15.5307 3.3512 10.0000 14.0758 15.5954 10.0000 28 16.1508 3.3903 10.0000 14.8787 15.7709 10.0000 29 16.7717 3.4166 10.0000 15.6887 15.9098 10.0000 30 17.3935 3.4302 10.0000 16.5036 16.0104 10.0000 31 18.0152 3.4294 10.0000 17.3232 16.0726 10.0000 32 18.6369 3.4150 10.0000 18.1445 16.0966 10.0000 33 19.2578 3.3863 10.0000 18.9657 16.0822 10.0000 34 19.8779 3.3432 10.0000 19.7853 16.0295 10.0000 35 20.4972 3.2865 10.0000 20.6026 15.9393 10.0000 36 21.1149 3.2139 10.0000 21.4142 15.8132 10.0000 37 21.7302 3.1269 10.0000 22.2195 15.6504 10.0000 38 22.3440 3.0239 10.0000 23.0168 15.4517 10.0000 39 22.9545 2.9066 10.0000 23.8045 15.2195 10.0000 40 23.5619 2.7749 10.0000 24.5818 14.9545 10.0000 41 24.1660 2.6273 10.0000 25.3480 14.6576 10.0000 42 24.7662 2.4645 10.0000 26.1022 14.3304 10.0000 43 25.3615 2.2873 10.0000 26.8420 13.9745 10.0000 44 25.9529 2.0950 10.0000 27.5690 13.5914 10.0000 45 26.5395 1.8883 10.0000 28.2809 13.1812 10.0000 46 27.1205 1.6672 10.0000 28.9785 12.7470 10.0000 47 27.6959 1.4326 10.0000 29.6608 12.2889 10.0000 48 28.2666 1.1844 10.0000 30.3272 11.8085 10.0000 49 28.8300 0.9226 10.0000 30.9777 11.3065 10.0000 50 29.3879 0.6480 10.0000 31.6121 10.7853 10.0000 51 29.9393 0.3607 10.0000 32.2306 10.2442 10.0000 52 30.4836 0.0607 10.0000 32.8332 9.6856 10.0000 53 31.0215 −0.2514 10.0000 33.4198 9.1101 10.0000 54 31.5523 −0.5754 10.0000 33.9904 8.5196 10.0000 55 32.0766 −0.9098 10.0000 34.5451 7.9130 10.0000 56 32.5930 −1.2554 10.0000 35.0854 7.2937 10.0000 57 33.1022 −1.6121 10.0000 35.6097 6.6616 10.0000 58 33.6049 −1.9785 10.0000 36.1197 6.0176 10.0000 59 34.0998 −2.3543 10.0000 36.6161 5.3631 10.0000 60 34.5874 −2.7398 10.0000 37.0998 4.6983 10.0000 61 35.0686 −3.1341 10.0000 37.5706 4.0247 10.0000 62 35.5419 −3.5371 10.0000 38.0303 3.3440 10.0000 63 36.0088 −3.9481 10.0000 38.4789 2.6552 10.0000 64 36.4685 −4.3671 10.0000 38.9170 1.9609 10.0000 65 36.9202 −4.7933 10.0000 39.3448 1.2594 10.0000 66 37.3663 −5.2267 10.0000 39.7638 0.5523 10.0000 67 37.8045 −5.6680 10.0000 40.1740 −0.1596 10.0000 68 38.2362 −6.1149 10.0000 40.5746 −0.8763 10.0000 69 38.6608 −6.5690 10.0000 40.9681 −1.5978 10.0000 70 39.0790 −7.0287 10.0000 41.3543 −2.3232 10.0000 71 39.4908 −7.4948 10.0000 41.7326 −3.0527 10.0000 72 39.8962 −7.9665 10.0000 42.1053 −3.7853 10.0000 73 40.2953 −8.4429 10.0000 42.4709 −4.5211 10.0000 74 40.6879 −8.9250 10.0000 42.8300 −5.2594 10.0000 75 41.0750 −9.4118 10.0000 43.1836 −6.0016 10.0000 76 41.4557 −9.9034 10.0000 43.5315 −6.7454 10.0000 77 41.8308 −10.3998 10.0000 43.8739 −7.4924 10.0000 78 42.2003 −10.8994 10.0000 44.2115 −8.2418 10.0000 79 42.5634 −11.4038 10.0000 44.5443 −8.9928 10.0000 80 42.9218 −11.9122 10.0000 44.8723 −9.7462 10.0000 81 43.2745 −12.4238 10.0000 45.1963 −10.5012 10.0000 82 43.6217 −12.9393 10.0000 45.5156 −11.2578 10.0000 83 43.9641 −13.4589 10.0000 45.8308 −12.0168 10.0000 84 44.3017 −13.9808 10.0000 46.1421 −12.7773 10.0000 85 44.6337 −14.5068 10.0000 46.2793 −13.1141 10.0000 86 44.7789 −14.7398 10.0000 46.3663 −13.3304 10.0000 87 44.8723 −14.8899 10.0000 46.4533 −13.5467 10.0000 88 44.9649 −15.0407 10.0000 46.5403 −13.7638 10.0000 89 45.0575 −15.1915 10.0000 46.6265 −13.9808 10.0000 90 45.1492 −15.3424 10.0000 46.7135 −14.1979 10.0000 91 45.2402 −15.4932 10.0000 46.7997 −14.4150 10.0000 92 45.3312 −15.6449 10.0000 46.8851 −14.6321 10.0000 93 45.4286 −15.7925 10.0000 46.9721 −14.8484 10.0000 94 45.5515 −15.9186 10.0000 47.0375 −15.0726 10.0000 95 45.6959 −16.0200 10.0000 47.0471 −15.3049 10.0000 96 45.8571 −16.0918 10.0000 46.9984 −15.5331 10.0000 97 46.0287 −16.1325 10.0000 46.8923 −15.7398 10.0000 98 46.2051 −16.1381 10.0000 46.7366 −15.9130 10.0000 99 46.3791 −16.1077 10.0000 46.5427 −16.0431 10.0000 100 46.5427 −16.0431 10.0000 0.1061 2.1852 20.0000 1 0.1061 2.1852 20.0000 −0.2538 2.9130 20.0000 2 0.5802 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8.1357 70.0000 24.7510 15.7406 70.0000 38 22.7662 7.7558 70.0000 25.2650 15.2482 70.0000 39 23.2155 7.3671 70.0000 25.7686 14.7446 70.0000 40 23.6592 6.9721 70.0000 26.2610 14.2306 70.0000 41 24.0966 6.5690 70.0000 26.7438 13.7079 70.0000 42 24.5283 6.1604 70.0000 27.2163 13.1756 70.0000 43 24.9537 5.7454 70.0000 27.6800 12.6361 70.0000 44 25.3735 5.3248 70.0000 28.1341 12.0878 70.0000 45 25.7877 4.8986 70.0000 28.5802 11.5331 70.0000 46 26.1963 4.4677 70.0000 29.0168 10.9713 70.0000 47 26.6002 4.0311 70.0000 29.4461 10.4030 70.0000 48 27.0000 3.5914 70.0000 29.8667 9.8292 70.0000 49 27.3943 3.1468 70.0000 30.2801 9.2498 70.0000 50 27.7845 2.6983 70.0000 30.6864 8.6656 70.0000 51 28.1708 2.2466 70.0000 31.0862 8.0766 70.0000 52 28.5531 1.7917 70.0000 31.4789 7.4828 70.0000 53 28.9322 1.3336 70.0000 31.8643 6.8851 70.0000 54 29.3073 0.8723 70.0000 32.2442 6.2833 70.0000 55 29.6784 0.4086 70.0000 32.6177 5.6768 70.0000 56 30.0471 −0.0575 70.0000 32.9848 5.0670 70.0000 57 30.4118 −0.5267 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96 40.9058 −15.7398 70.0000 42.0758 −15.3400 70.0000 97 41.0846 −15.7957 70.0000 41.9625 −15.5060 70.0000 98 41.2706 −15.8148 70.0000 41.8125 −15.6417 70.0000 99 41.4573 −15.7957 70.0000 41.6361 −15.7398 70.0000 100 41.6361 −15.7398 70.0000 4.0112 20.1133 80.0000 1 4.0112 20.1133 80.0000 4.0287 20.7773 80.0000 2 4.1852 19.5794 80.0000 4.2506 21.4054 80.0000 3 4.4972 19.1109 80.0000 4.6177 21.9617 80.0000 4 4.9042 18.7223 80.0000 5.0798 22.4429 80.0000 5 5.3743 18.4118 80.0000 5.6049 22.8547 80.0000 6 5.8843 18.1724 80.0000 6.1708 23.2091 80.0000 7 6.4182 17.9904 80.0000 6.7662 23.5100 80.0000 8 6.9641 17.8492 80.0000 7.3839 23.7638 80.0000 9 7.5148 17.7287 80.0000 8.0176 23.9737 80.0000 10 8.0654 17.6073 80.0000 8.6640 24.1429 80.0000 11 8.6129 17.4717 80.0000 9.3192 24.2721 80.0000 12 9.1572 17.3232 80.0000 9.9800 24.3623 80.0000 13 9.6975 17.1612 80.0000 10.6457 24.4158 80.0000 14 10.2338 16.9864 80.0000 11.3136 24.4310 80.0000 15 10.7654 16.7981 80.0000 11.9808 24.4086 80.0000 16 11.2921 16.5970 80.0000 12.6457 24.3512 80.0000 17 11.8140 16.3831 80.0000 13.3073 24.2594 80.0000 18 12.3304 16.1564 80.0000 13.9633 24.1349 80.0000 19 12.8412 15.9170 80.0000 14.6121 23.9777 80.0000 20 13.3456 15.6656 80.0000 15.2530 23.7901 80.0000 21 13.8452 15.4030 80.0000 15.8851 23.5738 80.0000 22 14.3376 15.1293 80.0000 16.5068 23.3320 80.0000 23 14.8252 14.8444 80.0000 17.1189 23.0638 80.0000 24 15.3057 14.5499 80.0000 17.7199 22.7725 80.0000 25 15.7805 14.2450 80.0000 18.3089 22.4589 80.0000 26 16.2490 13.9306 80.0000 18.8867 22.1245 80.0000 27 16.7111 13.6081 80.0000 19.4533 21.7702 80.0000 28 17.1676 13.2761 80.0000 20.0080 21.3982 80.0000 29 17.6177 12.9370 80.0000 20.5507 21.0104 80.0000 30 18.0623 12.5898 80.0000 21.0822 20.6057 80.0000 31 18.5004 12.2346 80.0000 21.6018 20.1860 80.0000 32 18.9338 11.8739 80.0000 22.1093 19.7518 80.0000 33 19.3615 11.5060 80.0000 22.6057 19.3057 80.0000 34 19.7837 11.1325 80.0000 23.0910 18.8468 80.0000 35 20.2011 10.7526 80.0000 23.5650 18.3767 80.0000 36 20.6129 10.3679 80.0000 24.0287 17.8962 80.0000 37 21.0208 9.9785 80.0000 24.4820 17.4054 80.0000 38 21.4238 9.5842 80.0000 24.9258 16.9066 80.0000 39 21.8228 9.1852 80.0000 25.3607 16.3998 80.0000 40 22.2179 8.7821 80.0000 25.7853 15.8851 80.0000 41 22.6089 8.3759 80.0000 26.2019 15.3631 80.0000 42 22.9960 7.9657 80.0000 26.6105 14.8340 80.0000 43 23.3791 7.5523 80.0000 27.0104 14.2993 80.0000 44 23.7590 7.1357 80.0000 27.4022 13.7590 80.0000 45 24.1357 6.7159 80.0000 27.7869 13.2131 80.0000 46 24.5092 6.2929 80.0000 28.1636 12.6616 80.0000 47 24.8795 5.8675 80.0000 28.5339 12.1061 80.0000 48 25.2466 5.4389 80.0000 28.8970 11.5459 80.0000 49 25.6105 5.0088 80.0000 29.2546 10.9816 80.0000 50 25.9729 4.5762 80.0000 29.6065 10.4142 80.0000 51 26.3320 4.1413 80.0000 29.9529 9.8436 80.0000 52 26.6887 3.7047 80.0000 30.2937 9.2690 80.0000 53 27.0431 3.2658 80.0000 30.6297 8.6919 80.0000 54 27.3958 2.8260 80.0000 30.9609 8.1117 80.0000 55 27.7462 2.3839 80.0000 31.2873 7.5291 80.0000 56 28.0950 1.9401 80.0000 31.6089 6.9441 80.0000 57 28.4413 1.4956 80.0000 31.9258 6.3567 80.0000 58 28.7861 1.0487 80.0000 32.2386 5.7662 80.0000 59 29.1285 0.6010 80.0000 32.5475 5.1740 80.0000 60 29.4693 0.1516 80.0000 32.8516 4.5802 80.0000 61 29.8093 −0.2985 80.0000 33.1524 3.9840 80.0000 62 30.1468 −0.7502 80.0000 33.4493 3.3855 80.0000 63 30.4828 −1.2027 80.0000 33.7430 2.7861 80.0000 64 30.8180 −1.6568 80.0000 34.0335 2.1844 80.0000 65 31.1516 −2.1117 80.0000 34.3200 1.5810 80.0000 66 31.4836 −2.5674 80.0000 34.6042 0.9769 80.0000 67 31.8148 −3.0239 80.0000 34.8851 0.3711 80.0000 68 32.1453 −3.4812 80.0000 35.1628 −0.2362 80.0000 69 32.4733 −3.9393 80.0000 35.4381 −0.8444 80.0000 70 32.8013 −4.3990 80.0000 35.7119 −1.4533 80.0000 71 33.1269 −4.8587 80.0000 35.9824 −2.0638 80.0000 72 33.4525 −5.3192 80.0000 36.2506 −2.6752 80.0000 73 33.7765 −5.7813 80.0000 36.5164 −3.2881 80.0000 74 34.0998 −6.2434 80.0000 36.7805 −3.9018 80.0000 75 34.4214 −6.7063 80.0000 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32.3998 5.7733 100.0000 71 28.9186 1.9330 100.0000 32.5762 5.1476 100.0000 72 29.2003 1.4820 100.0000 32.7510 4.5211 100.0000 73 29.4812 1.0311 100.0000 32.9226 3.8947 100.0000 74 29.7614 0.5794 100.0000 33.0918 3.2666 100.0000 75 30.0415 0.1277 100.0000 33.2586 2.6385 100.0000 76 30.3208 −0.3248 100.0000 33.4238 2.0096 100.0000 77 30.6002 −0.7765 100.0000 33.5858 1.3807 100.0000 78 30.8795 −1.2291 100.0000 33.7462 0.7502 100.0000 79 31.1588 −1.6816 100.0000 33.9042 0.1197 100.0000 80 31.4374 −2.1341 100.0000 34.0607 −0.5108 100.0000 81 31.7151 −2.5874 100.0000 34.2147 −1.1429 100.0000 82 31.9928 −3.0407 100.0000 34.3671 −1.7749 100.0000 83 32.2698 −3.4940 100.0000 34.5172 −2.4070 100.0000 84 32.5467 −3.9481 100.0000 34.6656 −3.0399 100.0000 85 32.8228 −4.4022 100.0000 34.7302 −3.3200 100.0000 86 32.9441 −4.6034 100.0000 34.7717 −3.4996 100.0000 87 33.0223 −4.7326 100.0000 34.8132 −3.6800 100.0000 88 33.1006 −4.8619 100.0000 34.8547 −3.8603 100.0000 89 33.1788 −4.9912 100.0000 34.8955 −4.0399 100.0000 90 33.2570 −5.1205 100.0000 34.9362 −4.2203 100.0000 91 33.3352 −5.2498 100.0000 34.9777 −4.4006 100.0000 92 33.4166 −5.3767 100.0000 35.0200 −4.5802 100.0000 93 33.5180 −5.4884 100.0000 35.0479 −4.7630 100.0000 94 33.6369 −5.5818 100.0000 35.0399 −4.9473 100.0000 95 33.7694 −5.6544 100.0000 34.9936 −5.1261 100.0000 96 33.9114 −5.7031 100.0000 34.9138 −5.2921 100.0000 97 34.0607 −5.7279 100.0000 34.8029 −5.4389 100.0000 98 34.2115 −5.7263 100.0000 34.6632 −5.5603 100.0000 99 34.3599 −5.6999 100.0000 34.5028 −5.6504 100.0000 100 34.5028 −5.6504 100.0000

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine rotor blade will be different than those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings. The disclosed loci of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction between other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

What is claimed is:
 1. A turbine rotor blade including an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape, wherein the airfoil shape lies in an envelope within +/−5% in a direction normal to any airfoil surface location.
 2. The turbine rotor blade as in claim 1, forming part of a stage of a turbine.
 3. The turbine rotor blade as in claim 1, wherein the turbine rotor blade forms a part of a second stage of turbine rotor blades of a turbine of a gas turbine.
 4. The turbine rotor blade as in claim 1, wherein a height of the turbine rotor blade is 10 inches to 40 inches.
 5. A turbine rotor blade including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil, wherein the suction-side airfoil shape lies in an envelope within +/−5% in a direction normal to any suction-side airfoil surface location.
 6. The turbine rotor blade as in claim 5, forming part of a stage of a turbine.
 7. The turbine rotor blade as in claim 5, wherein the turbine rotor blade forms a part of a second stage of turbine rotor blades of a turbine of a gas turbine.
 8. The turbine rotor blade as in claim 5, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches.
 9. A turbine comprising a turbine wheel having a plurality of turbine rotor blades, each of the turbine rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, wherein the suction-side airfoil shape lies in an envelope within +/−5% in a direction normal to any suction-side airfoil surface location.
 10. The turbine as in claim 9, wherein the turbine wheel comprises a stage of the turbine.
 11. The turbine as in claim 9, wherein X represents a distance parallel to the turbine axis of rotation.
 12. The turbine as in claim 9, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches.
 13. The turbine as in claim 9, wherein each of the turbine rotor blades includes an airfoil having a pressure-side airfoil shape, the airfoil having a nominal profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the pressure-side Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances by multiplying the pressure-side Cartesian coordinate values of X, Y and Z by a height of the airfoil, and wherein X and Y are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape, wherein the airfoil shape lies in an envelope within +/−5% in a direction normal to any airfoil surface location.
 14. The turbine as in claim 13, wherein the turbine rotor blade is a second stage turbine rotor blade.
 15. The turbine as in claim 11, wherein X represents a distance parallel to the turbine axis of rotation.
 16. The turbine as in claim 13, wherein a height of the turbine rotor blade is about 10 inches to about 40 inches. 